The tenfold-way topological phases have an Abelian group structure where the group operation is the direct sum “\(\oplus \) ” of two Hamiltonians [1]}, [2]}, [3]}.
Topological crystals constructed as decorations with tenfold-way topological phases inherit this Abelian group structure.
This allows to choose a set of generators from which all topological crystals can be constructed using the direct sum and symmetry-allowed deformations of the generating topological crystals.
